TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 487 ~ 4
9
3
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.1429
487
Re
cei
v
ed
Jan
uary 17, 201
5
;
Revi
sed Ma
rch 2
3
, 2015;
Acce
pted April 10, 2015
Spectrum Sensing Based on Monostable Stochastic
Resonance in Cognitive Radio Networks
Yonghua Wa
ng
1,2,3
, P
i
n Wan
2,4
*, Qin Deng
2
, Yuli Fu
1
1
School of Ele
c
tronic an
d Informatio
n
Engi
n
eeri
ng,
South
Chin
a Un
iversit
y
of T
e
chnolo
g
y
, Guan
gzh
ou
510
64
1, Guan
gdo
ng, Ch
ina
2
School of Aut
o
matio
n
, Guan
gdo
ng U
n
ivers
i
t
y
of
T
e
chnolo
g
y
, Gua
ngz
hou
5100
06, Guan
gdo
ng, Ch
ina
3
Hubei Ke
y
La
borator
y of Inte
llig
ent W
i
rel
e
ss
Communic
a
ti
o
n
s, South-Ce
nt
ral Univ
ersit
y
f
o
r Natio
nal
ities
,
W
uhan
43
007
4, Hube
i, Chin
a
4
Nationa
l Eng
i
neer
ing R
e
se
a
r
ch Center for
M
obil
e
Comm
u
n
icati
on, Guan
gzho
u 51
031
0,
Guang
do
ng, C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
w
a
np
in3
@
so
hu.com
A
b
st
r
a
ct
T
he cog
n
itive r
adi
o techn
o
l
o
g
y
can pr
ovid
e
dyna
mic spectr
um
access
and
improve t
he ef
ficienc
y
of spectru
m
uti
l
i
z
a
t
io
n. Spectr
um
se
nsi
ng is one of the key
technol
ogi
es
of cognitiv
e
ra
dio n
e
tw
orks.
T
h
e
spectru
m
sens
ing p
e
rfor
ma
n
c
e of
cogn
itiv
e radi
o netw
o
rks w
ill be
gr
eatly red
u
ce
d
in the low
S
NR
envir
onm
e
nt, especially when using en
ergy detection. Due to the monost
able
stochastic resonanc
e syst
em
can improve t
he ener
gy det
ection
system
output SNR, a m
o
nostable st
ochastic r
e
sonanceis applied t
o
spectru
m
s
ens
ing
bas
ed
on
the
ener
gy
det
ection
meth
o
d
of cog
n
itive
ra
dio
netw
o
rks i
n
this
pa
per. T
h
e
simulati
on r
e
su
lts show
that in
the low
SNR
e
n
viro
nm
ent, w
hen th
e fals
e a
l
ar
m pr
oba
bil
i
ty is consta
nt, t
h
e
prop
osed sp
ec
trum sens
in
g base
d
on
mon
o
stabl
e st
ocha
stic resona
nce
has better p
e
rformanc
e tha
n
traditio
nal e
ner
gy detectio
n
.
Ke
y
w
ords
: Mo
nostab
l
e Stoch
a
stic Reso
nan
ce, Cogn
itive R
adi
o, Spectru
m
Sensin
g, Ener
gy Detectio
n
1. Introduc
tion
Cog
n
itive rad
i
o (CR)
can
effectively allevi
ate the
co
ntradi
ction
b
e
twee
n the
spectrum
sho
r
tage a
n
d
the need
s o
f
the rapid d
e
velopme
n
t of wirele
ss communi
catio
n
[1]. Spectrum
sen
s
in
g (SS) is
o
ne of
the
key
te
chn
o
lo
gies
of CR
[2]
,[3]. The mai
n
functio
n
of spectrum
se
nsing
is to dete
c
t
spectrum h
o
le
s. So the
se
con
dary u
s
e
r
s (S
U)
ca
n a
c
cess to the
unu
sed
ch
an
nel
unde
r the
co
ndition that d
o
not cau
s
e i
n
terferen
ce
t
o
prim
ary u
s
ers (PU). At the same time
the
SU monito
r the prim
ary u
s
ers
so
as to b
e
able
to q
u
ickly exit when
the PU re
use
s
the ba
nd.O
n
e
of the
bigge
st
challen
g
e
s
for SS
is dete
c
ting the
we
ak PU
sign
al
in low Sign
al
to Noise Ra
tio
(SNR) environment. In low SNR environment, t
he performance
of spectrum
sensing will be
greatly re
du
ced [1]. In re
cent yea
r
s,
some
re
sea
r
che
r
s have prop
osed
th
e
appli
c
ation
of
stocha
stic re
son
a
n
c
e (S
R) to spe
c
trum
sen
s
ing
in
order to solve the problem o
f
detecting
weak
sign
al of the PU.
In [4], the bistable S
R
sy
stem is
appli
ed to the en
ergy dete
c
tio
n
in CR, in orde
r to
improve SNR. In sub
s
eq
uent studi
es,
He di ha
s a
l
so di
scusse
d how to ad
d an optimal
SR
noiseso that
it
can
improve
SNR maxim
a
lly [5].
They also
studie
d
the spe
c
tru
m
sen
s
in
g of
CR
based on Ch
aotic Stoch
a
s
tic Resona
n
c
e [6]. They al
so
confirme
d that the SR in the colo
red
noise environ
ment is
equal
ly applicable
[7]. K.
Zheng has
pro
p
o
s
ed
Block Spe
c
trum Sen
s
ing
a
n
d
Sequential S
pectrum Se
n
s
ing
sche
me
s of SR fors
p
e
ctru
m sen
s
i
ng in the
lo
w SNR
re
gime
[8].
Lin Yingpei h
a
s propo
se
d a spe
c
tru
m
sensi
ng sc
h
e
m
ein CRthat combi
ned the
cyclo
s
tation
ary
feature
dete
c
tion (CF
D
) a
nd S
R
[9]. Chen
Wei
in
o
r
de
r to
maxi
mizing
dete
c
t
i
on p
e
rfo
r
ma
nce,
has p
r
op
osed
a
gen
erali
z
e
d
SR meth
od
in th
e
lo
cal
sensi
ng
and
coope
rative
se
nsin
g [10]
-[11
].
In addition,
the cova
ria
n
ce
matrix [12],cyclo
station
a
ry
[9] and co
operative sp
ectru
m
sensi
n
g
[13]-[14] ba
sed on the
SR hav
e b
een confirm
ed that ca
n
improve
sp
ectru
m
sen
s
ing
perfo
rman
cei
n
a low SNR environ
ment.
The p
r
e
s
en
trese
a
rch
e
s on
sp
ectru
m
sen
s
ing
b
a
sed
on
SR are all
based on
traditional
bist
able SR, an
d the mono
stable sto
c
ha
st
ic re
son
a
n
c
e
is not involved. Due to t
he
mono
stable
SR
system
can im
prove
th
e outp
u
t SNR,
it is
appli
ed
to sp
ect
r
um
sensi
ngb
ase
d
on
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 487 – 49
3
488
the en
ergy
d
e
tection
met
hod
of CR
system in
ord
e
r to i
m
prove the
perfo
rmance u
nde
r low
SNRin thi
s
pa
per.
2. The Energ
y
Detection Model of Co
gniti
v
e
RadioBas
ed on S
t
och
astic
Re
sonan
c
e
Becau
s
e
the
energy dete
c
t
i
on ha
s th
e fo
llowing
adva
n
t
ages: n
eed
n
o
t to kn
ow
an
y prior
kno
w
le
dgeof the
PU,
low computation
a
l compl
e
xity
and ea
sy impl
ementation, t
hus it i
s
wide
ly
use
d
in
the
CR
spe
c
trum
sensi
ng. A
c
cording to
the
Neyman-Pe
arson crite
r
ia, sp
ectru
m
sen
s
i
n
g
probl
em can
be formul
ated
as the followi
ng two a
s
su
mptions:
0
1
:(
)
(
)
,
(0
,
1
,
.
.
.
,
1
)
:(
)
(
)
(
)
,
(0
,
1
,
.
.
.
,
1
)
Hr
t
n
t
tN
Hr
t
s
t
n
t
tN
(1)
Whe
r
e
1
H
indicat
e
s that the PU exists while
0
H
shows that the PU doe
s n
o
t exist.
()
rt
is
the received
sig
nal
of th
e SU.
()
s
t
is
the
PU sig
nal and
i
s
assu
medwith
zero
me
an an
d
var
i
anc
e
2
n
.
()
nt
den
otes the Ga
u
ssi
an noi
se a
nd is a
s
sume
d to be an i.i.dGau
ssian ra
ndom
pro
c
e
ss
with
zero mea
n
and varia
n
c
e
2
n
.The sig
nal
()
s
t
and t
he noi
se
()
nt
are
assume
dind
e
pend
ent of ea
ch othe
r.
Stochastic resonance refers
to the noi
se energy
will
be tran
sferred to the
signal energy
whe
n
the inp
u
t signal a
n
d
the noise h
a
v
e a match i
n
the non-li
n
ear sy
stem. At this time,
the
SNR
of the i
n
put si
gnal
will
not
be
lo
wered, but
will in
cre
a
se. Th
erefore
sto
c
ha
stic re
so
nan
ce
is
ideal fo
r
wea
k
sign
al d
e
tection proble
m
[
15].SR
syste
m
con
s
ist
s
of
three
elem
ent
s: am
ono
stab
le
or bista
b
le or multistabl
enonli
nea
r system, i
nput signal an
d
noise. Tra
d
i
tional
bista
b
le
SR
system mo
de
l is most wid
e
l
y usedin the
study.
It is describe
d
by a Lang
evin equ
ation [15]:
3
(
)
'
(
)
c
o
s
(2
)
(
)
(
)
(
)
c
o
s
(2
)
(
)
x
tV
x
A
f
t
n
t
a
x
t
b
x
t
A
f
t
n
t
(2)
W
h
er
e
cos
(
2
)
Af
t
is
the
input sign
al,
A
is the
sign
al a
m
plitude,
()
nt
is
the
s
t
oc
ha
s
t
ic
resona
nce
noisewith
th
e mea
n
o
f
0 an
d
varian
ce
2
n
S
R
n
o
is
e,
sat
i
sf
ie
s t
h
e
equatio
n
[(
)
(
)
]
2
(
)
En
t
n
t
D
t
,in whi
c
h
D
is the noise inten
s
ity.
24
()
24
ab
Vx
x
x
is
a
reflectio
n
of
the symmetric
sq
uare po
tential.
a
and
b
are the non
-l
inear
syste
m
unkn
o
wn
para
m
eters a
nd sati
sfy
0,
0
ab
.
The ene
rgy d
e
tection mo
d
e
l based on S
R
is
sho
w
n in
Figure 1 [5].
)
(
t
)
(
t
x
ED
SR
fa
P
)
(
t
r
)
(
0
t
r
Figure 1. The
energy dete
c
tion model ba
sed o
n
SR
3.
Spectr
u
m Sensing Ba
sed
on Ev
stigneev
T
y
pe Monosta
ble Stoc
hastic
Reso
nance
3.1. Monosta
ble SR s
y
stems
Evstigneev M
has
studie
d
a new
sin
g
le-stabl
e S
R
sy
stem- Evstig
n
eev(E) type
SR [16].
Pin W etc. h
a
ve studie
d
the SNR gain
of t
he Evstigneev type mono
stable SR, and co
nclu
de
d
that the SNR gain
can
be
gre
a
ter th
an
1 in a
ce
rtai
n re
gion th
ro
ugh a
d
ju
sting
the pa
ram
e
ters
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Spectrum
Sensin
g Base
d on Mono
stabl
e Stoc
ha
stic
Re
son
a
n
c
e in
…. (Yonghu
a Wan
g
)
489
[17]. The S
N
R gain
greater than 1 means
that th
e
o
u
tput SNR
greater t
han the input SNR
after
the sig
nal th
rough th
e Evstigneev type
SR sy
stem.
T
herefo
r
e, fo
r the en
ergy de
tector, d
e
tecti
on
perfo
rman
ce
can b
e
impro
v
ed by certai
n E type monostabl
e SR system.
In the case
of negle
c
ting
the ine
r
tial
effect, Lang
e
v
in equatio
n
of mono
stabl
e mod
e
l
prop
osed by [14] is:
()
'
(
)
c
o
s
(
2
)
(
)
x
tV
x
A
f
t
n
t
(3)
()
0
0
Vx
a
x
b
x
a
b
，，
(4)
Whe
r
e
()
Vx
is t
he
syste
m
po
tential functi
on,
cos
(
2
)
Af
t
is the d
r
i
v
e signal,
wh
en
applie
d in
th
e spe
c
trum
sensi
ng it i
s
t
he P
U
sign
al.
()
nt
is a
dditive
white
Gau
s
si
an n
o
ise
with
mean
0 a
n
d
varian
ce
1,
and
sati
sfie
s the
form
ula
[(
)
(
)
]
2
(
)
En
t
n
t
D
t
, Where
D
is t
he
noise intensity.
Whe
n
1
ab
,
3/
2
,
4
,
the potential function in (4)
do
es not exist any barrie
r
,
also d
o
e
s
not
exist the inflection poi
nt, Evst
igneev M thinks this i
s
a
kind of SR m
odel.
In [15], the mono
stable p
o
tential functio
n
is:
3/
2
4
21
()
0
34
Vx
a
x
b
x
a
b
，
(5)
Equation (5) i
s
d in equ
atio
n (3):
1/
2
3
()
(
)
-
c
o
s
(
2
)
(
)
x
ta
x
s
i
g
n
x
b
x
A
f
t
n
t
(6)
Whe
r
e
()
s
ign
x
is
the s
i
gn func
tion:
10
()
0
0
10
x
sign
x
x
x
，
，
，
(7)
Ref. [17] points out that whe
n
0.5
a
,
1
b
, and in the appro
p
riate fre
que
ncy ra
nge
,
Etype monost
able SR can
make the
system SNR gai
n greate
r
tha
n
1.
3.2.Energ
y
D
e
tec
t
ion Bas
e
d on Mono
stable S
R
3.2.1. Experimental Proc
edure
Dete
ction
pe
rforma
nce i
s
discu
s
sed
i
n
the
situati
on that
und
e
r
different
false
ala
r
m
prob
abilitie
s
condition
whil
e sam
e
SNR, and in th
e situatio
n that und
er dif
f
erent
SNR
while
same fal
s
e al
armprobabilit
y. The Monte Carl
o me
thod is used, specific
steps are
as follows:
1. Different false alarm pr
obabilities whil
e same S
N
R
(1) Acco
rdin
g
to bin
a
ry
hypothe
sis, th
e
re
ce
ived
sig
nal i
s
divid
e
d
into two
ca
ses:
0
H
and
1
H
. The
received
sign
al i
s
p
e
rfo
r
me
d
N
-p
oint
sam
p
ling, an
d the
n
p
r
o
c
e
s
sed
by sto
c
ha
stic
resona
nce sy
stem.
(2) A
cco
rdi
n
g to the energy
dete
c
ti
on pr
in
cipl
e, receive
d
si
gnale
nergy values
0
E
and
1
E
in
two hypothetical scenari
o
swe
r
e cal
c
ulate
d
,then
the
n
cyclescal
c
ulation
s
are
carrie
d
out.
(3)
After
n
cycles of calculations, the resulting
0
E
an
d
1
E
will
bestored in the array
01
02
0
3
0
[,
,
,
,
]
n
aE
E
E
E
and
11
1
2
13
1
[,
,
,
,
]
n
bE
E
E
E
.Then a
rray
01
02
0
3
0
[,
,
,
,
]
n
aE
E
E
E
is arra
n
ged in
ascen
d
ing o
r
der, and b
e
saved to anoth
e
r array
12
3
[,
,
,
,
]
n
as threshold valu
e
s
.
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 487 – 49
3
490
(4) Calculate
the n
u
mbe
r
s that the
ele
m
ents i
n
the
array
01
02
0
3
0
[,
,
,
,
]
n
aE
E
E
E
greate
r
than the t
h
re
shol
d
valu
e
12
3
,,
,
,
n
re
sp
ectiv
e
ly, then
obtaine
d
12
3
[,
,
,
,
]
n
LL
L
L
L
.
12
3
[/
,
/
,
/
,,
/
]
n
Ln
L
n
L
n
L
n
rep
r
e
s
ent
s a
set
of false
alarm
probability
12
3
[,
,
,
,
]
fa
fa
f
a
fa
fa
n
PP
P
P
P
,where
[0
,
1
]
fa
P
.
(5)
Cal
c
ulate
the numbers that
the elements in th
e array
11
1
2
13
1
[,
,
,
,
]
n
bE
E
E
E
great
er
than the
thresh
old
value
12
3
,,
,
,
n
re
sp
ectively
, then
obtai
ned
12
3
[,
,
,
,
]
n
M
MM
M
M
.
12
3
[/
,
/
,
/
,
,
/
]
n
M
nM
n
M
n
M
n
rep
r
e
s
ent
s a
set
of dete
c
tion
pro
babi
lity
12
3
[,
,
,
,
]
dd
d
d
d
n
PP
P
P
P
.
12
3
,,
,
,
dd
d
d
n
PP
P
P
represent t
he detection performance
when fal
s
e alarm probabilities are
12
3
,,
,
,
fa
fa
f
a
fa
n
PP
P
P
unde
r the sa
me SNR e
n
vironm
ent.
2 .Con
stant false al
arm p
r
obability und
er differe
nt SNR e
n
viron
m
ent
Steps (1
), (2
), (3) an
d (4
) are same a
s
ab
ove.
(5)
Under the condition of constant fa
lse-alarm probability,
the subscri
p
t of
in the
array
12
3
[,
,
,
,
]
n
is re
pre
s
ente
d
by.
u
is the corre
s
p
o
nding e
nergy detection thresh
old in a
given false-al
arm p
r
ob
abili
ty. After n times
cal
c
ulati
ons, the
re
sulting en
ergy
values
1
E
are
saved to
array
11
1
2
13
1
[,
,
,
,
]
n
bE
E
E
E
.Then the numbe
r
M
that th
e
element
s
of
11
12
13
1
[,
,
,
,
]
n
bE
E
E
E
greate
r
tha
n
u
is cal
c
ulate
d
.
/
M
n
is the dete
c
tion proba
bil
i
ty
d
P
.
(6) Repeat steps (1) to (5) different SNR
environments, the detec
tion probabilities can
be obtain
ed u
nder the e
n
vironment
s with
con
s
t
ant false alarm p
r
ob
ability and different SNR.
3.2.2. Simula
tion results
Usi
ng MATL
AB7.1 establ
ish the
simu
lation enviro
n
ment. Ch
an
nel interfe
r
e
n
ce
an
d
fading effect
is not take
n into accou
n
t in
this paper. Assume
that the signal of the PU
is
cos
(
2
)
Af
t
,
Gaussi
an white
noise i
s
()
t
. Where
4
,
2
2
ni
A
SNR
,
the noise vari
ance
2
1
n
,
f
are
0.01Hz, 0.05
Hz, 0.
2Hz re
spe
c
tively.
Sampling fre
quen
cy
128
s
f
f
.Sampling p
o
int
256
N
. The nu
mbe
r
of
Monte
Ca
rlo
simulatio
n
s
is 100
0. Com
pare th
e tradi
tional ene
rgy
detection
m
e
thod an
d en
ergy dete
c
tio
n
method b
a
s
ed
on E type m
ono
stable S
R
p
e
rfo
r
man
c
e
und
er t
w
o
co
ndition
s t
hat at the
sa
me SNR
different
false ala
r
m
proba
bility environme
n
t
and con
s
t
ant false al
arm proba
bil
i
tydifferent SNR
environ
ment. The re
sult
s are sho
w
n in Fi
gure 2,3,4,5
resp
ectively.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
Pf
Pd
f
=
0.
01
H
z
tr
a
d
i
t
i
ona
l
E
D
f
=
0.
01
H
z
E
ty
pe m
o
n
o
s
t
a
b
l
e
S
R
f
=
0.
05
H
z
tr
a
d
i
t
i
ona
l
E
D
f
=
0.
05
H
z
E
ty
pe m
o
n
o
s
t
a
b
l
e
S
R
f
=
0.
2H
z
t
r
ad
i
t
i
o
nal
E
D
f
=
0.
2H
z
E
t
y
p
e
m
ono
s
t
ab
l
e
S
R
Figure 2. RO
C cu
rves of t
w
o metho
d
s
unde
r differe
nt frequen
cie
s
whil
e SNR=-15dB
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TELKOM
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ISSN:
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930
Spectrum
Sensin
g Base
d on Mono
stabl
e Stoc
ha
stic
Re
son
a
n
c
e in
…. (Yonghu
a Wan
g
)
491
As ca
n be
seen fro
m
the
Figure 2, 3, in
the co
nd
ition of SNR=-1
5dB a
nd
SNR=-
20dB,
the pe
rforman
c
e
of t
he tra
d
itional
energy
dete
c
tion is almo
st
the
same
when th
e
sign
al
freque
ncy
f
are 0.01Hz, 0.0
5
Hz, and 0.2
H
z. Thi
s
is
b
e
c
au
se the tra
d
itional
ene
rg
y detection is
freque
ncy i
n
d
epen
den
ce.
The p
e
rfo
r
ma
nce
o
f ene
rgy
detectio
n
ba
sed on
E type
mono
stable
SR
cha
nge
s wh
en the fre
q
u
ency
cha
nge
s an
d this p
e
rform
a
n
c
ea
re highe
r tha
n
the traditio
nal
energy detection method
s. The detecti
on pe
rforma
nce i
s
the lowe
stwhen
0.01
f
Hz
an
dthe
detectio
n
pe
rforma
nce is th
e highe
st
wh
en
0.05
f
Hz
. This sh
o
w
s th
at
thesi
gnal
freq
uen
cy
has
a certai
n effect on the ene
rgy detection
based on E type mono
stabl
e SR.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
Pf
Pd
f
=
0
.
0
1
H
z
t
r
a
d
it
io
n
a
l E
D
f
=
0.
01H
z
E
t
y
pe m
onos
t
abl
e S
R
f
=
0
.
0
5
H
z
t
r
a
d
it
io
n
a
l E
D
f
=
0.
05H
z
E
t
y
pe m
onos
t
abl
e S
R
f
=
0.
2H
z
t
r
ad
i
t
i
ona
l
E
D
f
=
0.
2H
z
E
t
y
pe m
o
nos
t
abl
e S
R
Figure 3. RO
C cu
rves of t
w
o metho
d
s
unde
r differe
nt frequen
cie
s
whil
e SNR=-20 dB
-2
0
-1
8
-1
6
-1
4
-1
2
-10
-8
-6
-4
-2
0
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
SN
R
Pd
f
=
0.
01 t
r
adi
ti
o
nal
E
D
f
=
0.
01 E
t
y
pe m
onos
ta
bl
e S
R
f
=
0.
05 t
r
adi
ti
o
nal
E
D
f
=
0.
05 E
t
y
pe m
onos
ta
bl
e S
R
f
=
0.
2 tr
adi
t
i
on
al
E
D
f
=
0.
2 E
ty
pe m
o
nos
t
a
b
l
e S
R
Figure 4. Det
e
ction probability
versus S
NR under different
f
when
0.05
fa
P
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ISSN: 16
93-6
930
TELKOM
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Vol. 13, No. 2, June 20
15 : 487 – 49
3
492
-2
0
-1
8
-1
6
-1
4
-1
2
-1
0
-8
-6
-4
-2
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
SN
R
Pd
f
=
0.01 tr
a
d
i
t
i
onal
E
D
f
=
0.01
E
ty
pe
m
o
n
o
s
t
abl
e S
R
f
=
0.05
tr
adi
ti
onal
E
D
f
=
0.05
E
ty
pe
m
o
n
o
s
t
abl
e S
R
f
=
0.2 tr
ad
i
t
i
onal
E
D
f
=
0.2 E
ty
pe m
ono
s
t
abl
e S
R
Figure 5.Dete
ction proba
bil
i
ty versus
SNR und
er differentfrequ
en
cie
s
wh
en
0.1
fa
P
As can
be
seen from the
Figure 4,
5, in t
he differe
nt
SNRenviro
n
ment, the
d
e
tectio
n
perfo
rman
ce
ofthe traditio
nal
ene
rgy d
e
tection
i
s
al
most
the
sa
me wh
en
f
chang
es. It al
so
sho
w
s
that
th
e traditional e
nergy
dete
c
tion met
hod
is
sign
al fre
que
ncyind
epen
d
ence
agai
n. T
h
e
perfo
rman
ce
of ene
rgy
det
ection
ba
se
d
on E type
mo
nosta
ble S
R
cha
nge
s
wh
e
n
the f
r
eq
uen
cy
cha
nge
s
and
this p
e
rfo
r
ma
nce
a
re
hig
h
e
r
tha
n
the
co
nventional
en
ergy
dete
c
tio
n
meth
od
s. T
he
d
e
t
e
c
tion
per
fo
r
m
an
ce
is th
e
low
e
s
t
w
h
en
0.01
f
Hz
andthe
dete
c
tion
p
e
rform
a
n
c
e
is the
highe
st wh
en
0.05
f
Hz
.When
0.
02
f
Hz
the d
e
tection
pe
rfo
r
man
c
e
i
s
sli
ghtly lowe
r th
an that
whe
n
0.05
f
Hz
.
4. Conclusio
n
s
In this pape
r,
an Evstigne
ev-type mono
stable
s
to
cha
s
tic re
sona
nce
system is a
p
p
lied to
energy dete
c
tion of spe
c
trum se
nsi
ng i
n
ord
e
r
to in
cre
a
se the
system output
SNR, there
b
y
enha
nci
ng the low SNR e
n
vironm
ent energy dete
c
ti
on perfo
rma
n
c
e. Simulatio
n
results sh
o
w
that in
the case of
constant
false
alarm prob
ability, the detection
probability of energy
detecti
on
based on m
ono
stable S
R
is hig
h
e
r
than that of
the tradition
al ene
rgy
de
tection meth
od,
esp
e
ci
ally in
low S
N
R envi
r
onm
ent. Thi
s
resea
r
ch wi
ll bro
ade
n th
e sco
pe of
a
pplication of
SR
and can in
cre
a
se the d
e
tection prob
abilit
y of spectrum
sen
s
ing u
n
d
e
r low S
NR e
n
vironm
ent.
Ackn
o
w
l
e
dg
ements
This
wo
rk
was
sup
porte
d
by the Chi
n
a Po
stdo
cto
r
al Scien
c
e
F
ound
ation (G
rant No
.
2014M
552
52
9) a
nd the
Youth Fo
undatio
n of
G
uan
gdo
n
g
Unive
r
sity of Techno
logy
(No.1
3
Q
N
Z
D
006).
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ei W
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930
Spectrum
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Re
son
a
n
c
e in
…. (Yonghu
a Wan
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